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Can someone help me with this question please :) (University)

Can someone help me with this question please :) (University)-example-1
User Kenshinji
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5.9k points

1 Answer

3 votes

Answer:

(-5 1 0 0) and (-3 0 1 0)

Explanation:

Based on my memory, you can use the dot product to find orthogonality meaning

u1 . u2 = 0

In this case, we let u be the arbitrary vector represented by (x y z w)

u . (1 5 3 0) can be expressed as an equation given by:

(x y z w)

We solve this equation letting y = s and z = t and x = -5s -3t

Reconstruct this according to their variable will give

(-5 1 0 0)s + (-3 0 1 0)t = 0

So the basis vectors are (-5 1 0 0) and (-3 0 1 0).

Let c1 and c2 be arbitrary constants:

if you solve for c1(-5 1 0 0) + c2(-3 0 1 0) = 0

c1 and c2 should have only trivial solution, which proves its

linear independence and so it forms a basis vector space.

User VStoykov
by
7.0k points
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